USING MICROSOFT EXCEL TO MODEL A TENNIS MATCH
|
|
- Moses Campbell
- 7 years ago
- Views:
Transcription
1 USING MICROSOFT EXCEL TO MODEL A TENNIS MATCH Tristan J. Barnett and Stephen R. Clarke School of Mathematical Sciences Swinburne University PO Box 218 Hawthorn Victoria 3122, Australia tbarnett@groupwise.swin.edu.au sclarke@groupwise.swin.edu.au Abstract This paper demonstrates the use of Microsoft Excel to generate the probability of winning and mean length of the remainder of the match conditional on the state of the match. Previous models treat games, sets and matches independently. We show how a series of interconnected sheets can be used to repeat these results. We also set up a sheet which can give the required statistics using the full match, set and game score as the state. The exercise could form an interesting and useful teaching example, and allow students to investigate the properties of tennis scoring systems. 1 Introduction Many papers have investigated the characteristics of various scoring systems, particularly in racquet sports. The game of Lawn Tennis has a history of changing formats. Although it uses a basic nested system of points, games, sets and matches, there is much variation within that basic structure. Matches can be one set, or best of three or five sets, sets can be first to six, eight or ten games, advantage or non advantage, and games can be the traditional four point advantage, or seven or ten point tiebreakers. We even have the recent innovation at the 2001 Australian Open mixed, where the third set becomes a single tiebreaker game. This innovation is extending into the Victorian Tennis Association pennant this year. The basic principles involved in modelling a tennis match are well known, and a Markov chain model with a constant probability of winning a point was set up by Schutz [4]. While such a model is acceptable within a game, a model which allows a player a different probability of winning depending on whether they are serving or receiving is essential for tennis. Statistics of interest are usually the chance of each player winning, and the expected length of the match. Croucher [1] looks at the conditional probabilities for either player winning a single game from any position. Pollard [3] uses a more analytic approach to calculate the probability for either player winning a game or set along with the expected number of points or games to be played and their corresponding variance. Most of the previous work uses analytical methods, and treats each scoring unit independently. This results in limited tables of statistics. Thus the chance of winning a game and the expected number of points remaining in the game is calculated at the various scores within a game. The chance of winning a set and the expected number of games remaining in the set is calculated only after a completed game and would not show for example the probability of a player s chance of winning from three games to two,
2 2 T.J. Barnett and S.R. Clarke This paper discusses the use of Microsoft Excel to repeat these applications using a set of interrelated spreadsheets. This allows any probabilities to be entered and the resultant statistics automatically calculated or tabulated. In addition, more complicated workbooks can be set up which allow the calculation of the chance of winning a match and the expected number of points in the remainder of the match at any stage of the match given by the match, set and game score. These allow the dynamic updating of player s chances as a match progresses. 2 Simple Model We explain the method by first looking at the simple model where we have two player s, A and B, and player A has a constant probability p of winning a point. We set up a Markov chain model of a game where the state of the game is the current game score in points (thus is 3-2). With probability p the state changes from a, b to a + 1, b and with probability 1 p it changes from a, b to a, b + 1. Thus if P (a, b) is the probability that player A wins when the score is (a,b), we have: P (a, b) = pp (a + 1, b) + (1 p)p (a, b + 1) The boundary values are P (a, b) = 1 if a = 4, b 2, P (a, b) = 0 if b = 4, a 2. The boundary values and formula can be entered on a simple spreadsheet. The problem of deuce can be handled in two ways. Since deuce is logically equivalent to 30-30, a formula for this can be entered in the deuce cell. This creates a circular cell reference, but the iterative function of Excel can be turned on, and Excel will iterate to a solution. Alternatively, it is easily shown that the chance of winning from deuce is: p 2 p 2 + (1 p) 2 Entering this formula removes the need for iteration. Table 1 shows the results obtained, using a value of p = It indicates that a player with a 54% chance of winning a point has a 60% chance of winning the game. Note that since advantage server is logically equivalent to 40-30, and advantage receiver is logically equivalent to 30-40, the required statistics can be found from these cells. The mean number of points in the remainder of the game is handled similarly as shown in Table 2. All boundary points become 0, the recurrence relation becomes: M(a, b) = 1 + pm(a + 1, b) + (1 p)m(a, b + 1) The formula for deuce is: 2 p 2 + (1 p) game B score game Table 1: The conditional probabilities of A winning the game from various scorelines A similar spreadsheet can be set up for a set. The constant probability of winning a game can be obtained from the (0,0) cell of the previous sheet. Similarly for a match. Thus we obtain six connected
3 Using Microsoft Excel to model a tennis match game B score game Table 2: The expected number of points remaining in a game from various scorelines sheets - entering the chance of winning a point results in the chance of winning a game and expected number of points in the remainder of the game conditional on the game score, the chance of winning a set and expected number of games in the remainder of the set conditional on the set score, and the chance of winning a match and expected number of sets in the remainder of the match conditional on the match score. In this case, the sheet suggests a player with a 54% chance of winning a point, has a 59.9% chance of winning a game, a 76.3% chance of winning a tiebreak set, a 85.9% chance of winning a 3 set match and a 91% chance of winning a five-set match. Excel has excellent facilities for building up one or two way tables. Table 3 shows some of the match statistics for chances and expected lengths of winning games, sets and matches with the probability of winning a point ranging from 0.5 to 1. We will use the following notation: p(game) = probability of winning a game M(Game) = expected number of points in a game p(set) = probability of winning a tiebreak set M(Set) = expected number of games in a tiebreak set p(match) = probability of winning a 5 set match M(Match) = expected number of sets in a 5 set match Magnus and Klassen [2] tested some often-heard hypotheses relating to the service in tennis. They collected data on 481 matches played in the men s singles and women s singles championships at Wimbledon from 1992 to We will compare some of their statistics with our model. In men s singles with two seeded player s, on service they won 67% of the points and 86% of the games. In women s singles with two seeded player s, on service they won 57% of the points and 67% of the games. Both these results agree with our model as highlighted in Table 3. 3 Two parameter model For more realistic models the process is essentially the same, just a little more complicated. We now have 2 parameters where: p A = probability of A winning a point if A is serving p B = probability of B winning a point if B is serving Since the chance of a player winning now depends on who is serving, we need to introduce this into the state description. The state of a game becomes the score and whether the player is serving or receiving. Thus we need two sheets for a game, one for player A serving and one for player B serving. Similarly we need two sheets for the set score, and one for the match score. The formula and boundary conditions are similar. The main difference is that adjacent cells in terms of the Markov chain are not necessarily adjacent on the spreadsheet, since players alternate service games. We will also use the following notation: p A p B = probability of A winning a game if A is serving = probability of B winning a game if B is serving
4 4 T.J. Barnett and S.R. Clarke p p(game) M(Game) p(set) M(Set) p(m atch) M(M atch) Table 3: Match statistics depending on the probability of winning a point The following probabilities are applied: p A = 0.6, p B = 0.58 The conditional probabilities for an advantage set are given in Tables 4 and 5 for each player serving. The probability of A winning an advantage set from 6 games all - A or B serving is: p A p B 1 p A p B + (1 p A )(1 p B ) By substituting p A = 0.6 in our simple model, p A = Similarly by letting p B = 0.58, p B = Substituting these figures into the equation above gives B score Table 4: The conditional probabilities of A winning an advantage set from various games scores if A is serving As expected 6-6 = 5-5 = 4-4 regardless of who is serving. Also worth noting is that P (winning set a score with an even number of games with A serving) = P (winning set a score with an even number of games with B serving). 4 Six parameter model Instead of building up independent sheets linked through the probability of winning a point, game or set, we can build a model in which the state of the game is match score, set score, game score and whether
5 Using Microsoft Excel to model a tennis match B score Table 5: The conditional probabilities of A winning an advantage set from various game scores if B is serving the player is serving or receiving. Also included is first and second serves. With this model, a typical question could be: What is the probability of player A winning a five set match with the current score at 2 sets to 1, 3 games to 4, and fault one? We now have 6 parameters: 1st serve % for each player, winning % on first serve for each player and winning % on second serve for each player. The same techniques of deriving a formula for the last point of a game or set and allowing recurrence relations to work out the remaining points are applied. We will take the statistics from the 2002 Australian Open men s singles final, where Thomas Johannson defeated Marat Safin (7-4) Let Johannson = player A, Safin = player B 1st serve % for player A = 56% 1st serve % for player B = 63% Winning % on 1st Serve for player A = 86% Winning % on 1st Serve for player B = 67% Winning % on 2nd Serve for player A = 53% Winning % on 2nd Serve for player B = 54% Table 6 represents the conditional probabilities of player A winning a 5 set match at a set all, 4-4 in the 3rd set with player A serving. It highlights the importance of a 1st serve on certain points. At a 1st serve in would give a 77% chance of winning the match, whereas fault drops to 74%. Particularly in tiebreaks, this margin has greater emphasis to the outcome of a match. 0 0/2nd 15 15/2nd 30 30/2nd 40 40/2nd game B score game Table 6: Conditional probabilities of winning a game from various scorelines 5 Conclusions Through the use of Excel we have shown how to produce the conditional probabilities of either player winning the match and the expected number of points, games and sets remaining from any position
6 6 T.J. Barnett and S.R. Clarke within the match. The use of if statements often used in Excel would allow us to enter what type of match it is (tiebreaker of advantage, 3 or 5 sets) and the current position in the match, to give us the corresponding probabilities and the expected length remaining. This idea would make accessible the relevant statistics for a match in progress. Microsoft Excel now incorporates Visual Basic for Applications (VBA), enabling the modelling of a tennis match to be powerful and still relatively easy to implement. References [1] J.S. Croucher, The conditional probability of winning games of tennis, Res. Quart. for Exercise and Sport, 57(1) (1986), [2] J.R. Magnus and F.J.G.M Klaassen, On the advantage of serving first in a tennis set: four years at Wimbledon. The Statist., 48(2) (1999), [3] G.H. Pollard, An analysis of classical and tie-breaker tennis. Austral. J. Statist., 25 (1983), [4] R.W. Schutz, A mathematical model for evaluating scoring systems with specific reference to tennis. Res. Quart. for Exercise and Sport, 41 (1970),
Predicting a tennis match in progress for sports multimedia
Predicting a tennis match in progress for sports multimedia Tristan Barnett University of South Australia School of Mathematics and Statistics strategicgames@hotmail.com Abstract This paper demonstrates
More informationCombining player statistics to predict outcomes of tennis matches
IMA Journal of Management Mathematics (2005) 16, 113 120 doi:10.1093/imaman/dpi001 Combining player statistics to predict outcomes of tennis matches TRISTAN BARNETT AND STEPHEN R. CLARKE School of Mathematical
More informationDEVELOPING A MODEL THAT REFLECTS OUTCOMES OF TENNIS MATCHES
DEVELOPING A MODEL THAT REFLECTS OUTCOMES OF TENNIS MATCHES Barnett T., Brown A., and Clarke S. Faculty of Life and Social Sciences, Swinburne University, Melbourne, VIC, Australia ABSTRACT Many tennis
More informationTennis Winner Prediction based on Time-Series History with Neural Modeling
Tennis Winner Prediction based on Time-Series History with Neural Modeling Amornchai Somboonphokkaphan, Suphakant Phimoltares, and Chidchanok Lursinsap Abstract Tennis is one of the most popular sports
More informationMATHEMATICAL MODELLING IN HIERARCHICAL GAMES WITH SPECIFIC REFERENCE TO TENNIS
MTHEMTICL MODELLING IN HIERRCHICL GMES WITH SPECIFIC REFERENCE TO TENNIS y Tristan J. arnett THESIS SUMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY T SWINURNE UNIVERSITY MRCH 2006 c Copyright by Tristan
More informationInferring Tennis Match Progress from In-Play Betting Odds : Project Report
Inferring Tennis Match Progress from In-Play Betting Odds : Project Report James Wozniak 4th year Information Systems Engineering MEng jhw107@ic.ac.uk Supervised by Dr. William Knottenbelt June 23, 2011
More informationTeaching Mathematics and Statistics Using Tennis
Teaching Mathematics and Statistics Using Tennis Reza Noubary ABSTRACT: The widespread interest in sports in our culture provides a great opportunity to catch students attention in mathematics and statistics
More informationDOUBLES TENNIS LEAGUE
DOUBLES TENNIS LEAGUE *The following rules provided by Purdue Intramural Sports are not meant to be all encompassing. Please refer to the Participant Manual for comprehensive eligibility guidelines, policies,
More informationDOUBLES TENNIS LEAGUE *The following rules provided by Purdue Intramural Sports are not meant to be all encompassing.*
DOUBLES TENNIS LEAGUE *The following rules provided by Purdue Intramural Sports are not meant to be all encompassing.* SECTION 1. TOURNAMENT FORMAT I. League Overview A. The league will consist of a five
More informationThe Tennis Formula: How it can be used in Professional Tennis
The Tennis Formula: How it can be used in Professional Tennis A. James O Malley Harvard Medical School Email: omalley@hcp.med.harvard.edu September 29, 2007 1 Overview Tennis scoring The tennis formula
More informationSINGLES TENNIS RULES
TEAM SINGLES INTRAMURAL SPORTS Mission Statement: The mission of the Department of Campus Recreation is to develop and provide high quality innovative fitness, recreation, and leadership programming to
More informationTEAM TENNIS TOURNAMENT *The following rules provided by Purdue Intramural Sports are not meant to be all encompassing.*
TEAM TENNIS TOURNAMENT *The following rules provided by Purdue Intramural Sports are not meant to be all encompassing.* SECTION 1. LEAGUE FORMAT I. Tournament Overview A. The tournament will consist of
More informationBetting on Excel to enliven the teaching of probability
Betting on Excel to enliven the teaching of probability Stephen R. Clarke School of Mathematical Sciences Swinburne University of Technology Abstract The study of probability has its roots in gambling
More informationHOW TO BET ON TENNIS. Gambling can be addictive. Please play responsibly. http://responsiblegambling.betfair.com
HOW TO BET ON TENNIS Gambling can be addictive. Please play responsibly. http://responsiblegambling.betfair.com Tennis is great for Betfair customers as it takes place over 11 months of the year, which
More informationSECTION A OFFICIAL EVENTS
1 The Official Special Olympics Sports Rules for Tennis shall govern all Special Olympics competitions. As an international sports program, Special Olympics has created these rules based upon International
More informationInstructions for Authors. 1. Scope
Instructions for Authors 1. Scope The International Journal of Performance Analysis in Sport is published on behalf of the Centre for Performance Analysis, Cardiff School of Sport at Cardiff Metropolitan
More informationSpring Doubles Tennis Rules
Spring Doubles Tennis Rules USTA Tennis Rules Condensed USTA Rules may be modified for IM Play at the discretion of the Intramural Sports Office RULE 1: The Court The court shall be a rectangle, 78 feet
More informationThursday, October 18, 2001 Page: 1 STAT 305. Solutions
Thursday, October 18, 2001 Page: 1 1. Page 226 numbers 2 3. STAT 305 Solutions S has eight states Notice that the first two letters in state n +1 must match the last two letters in state n because they
More informationComplement. If A is an event, then the complement of A, written A c, means all the possible outcomes that are not in A.
Complement If A is an event, then the complement of A, written A c, means all the possible outcomes that are not in A. For example, if A is the event UNC wins at least 5 football games, then A c is the
More informationCurrent California Math Standards Balanced Equations
Balanced Equations Current California Math Standards Balanced Equations Grade Three Number Sense 1.0 Students understand the place value of whole numbers: 1.1 Count, read, and write whole numbers to 10,000.
More informationInferring the score of a tennis match from in-play betting exchange markets
Inferring the score of a tennis match from in-play betting exchange markets A. Gabriela Irina Dumitrescu*, B. Xinzhuo Huang**, C. William Knottenbelt***, D. Demetris Spanias****, E. James Wozniak*****
More informationA SET-BY-SET ANALYSIS METHOD FOR PREDICTING THE OUTCOME OF PROFESSIONAL SINGLES TENNIS MATCHES
4th year Software Engineering MEng project A SET-BY-SET ANALYSIS METHOD FOR PREDICTING THE OUTCOME OF PROFESSIONAL SINGLES TENNIS MATCHES June 17, 2012 Agnieszka M. Madurska amm208@doc.ic.ac.uk Imperial
More informationPercentage Play in Tennis
Percentage Play in Tennis G. Edgar Parker Abstract Tennis scoring makes tennis different from most games in that scoring at the point level is not cumulative and it is thus possible for a player scoring
More informationMelbourne Sports & Aquatic Centre SOCIAL COMPETITIONS - ALL SEASONS Rules and Regulations 2013
Melbourne Sports & Aquatic Centre SOCIAL COMPETITIONS - ALL SEASONS Rules and Regulations 2013 1. Venue: Melbourne Sports & Aquatic Centre (MSAC) Aughtie Drive, Albert Park 2. Times Played: Monday: A,
More informationPool Play and Playoff Formats: 14 Teams
Pool Play and Playoff Formats: 14 Teams Pool play format: 4 courts, 6 referees, 14 Teams, 33 matches 2 pools of 4 teams, 2 pools of 3 teams 4-team pools Match 1 1 vs. 3 (2) For pools of 3 or 4 teams, the
More informationBEE Calculations Content
BEE Calculations Content How the scorecard works Basic calculation of Ownership using the following methods: 1. Control principal 2. Strict flow through principal 3. Modified flow through principal Sale
More informationOBJECTIVE ASSESSMENT OF FORECASTING ASSIGNMENTS USING SOME FUNCTION OF PREDICTION ERRORS
OBJECTIVE ASSESSMENT OF FORECASTING ASSIGNMENTS USING SOME FUNCTION OF PREDICTION ERRORS CLARKE, Stephen R. Swinburne University of Technology Australia One way of examining forecasting methods via assignments
More informationRaising Interest in Statistics through Sporting Predictions on the Internet
Raising Interest in Statistics through Sporting Predictions on the Internet Stephen R Clarke School of Mathematical Sciences Swinburne University of Technology PO Box 218, John St, Hawthorn, Australia
More informationWORKED EXAMPLES 1 TOTAL PROBABILITY AND BAYES THEOREM
WORKED EXAMPLES 1 TOTAL PROBABILITY AND BAYES THEOREM EXAMPLE 1. A biased coin (with probability of obtaining a Head equal to p > 0) is tossed repeatedly and independently until the first head is observed.
More informationPLAYING RULES & FORMAT
WDF EUROPE CUP PLAYING RULES & FORMAT Seventh revised edition A Full Member of the SPORTACCORD and committed to compliance with the WADA Code on Anti-Doping. Random drug testing could occur in this event
More informationIntro to Simulation (using Excel)
Intro to Simulation (using Excel) DSC340 Mike Pangburn Generating random numbers in Excel Excel has a RAND() function for generating random numbers The numbers are really coming from a formula and hence
More informationApplying the Kelly criterion to lawsuits
Law, Probability and Risk (2010) 9, 139 147 Advance Access publication on April 27, 2010 doi:10.1093/lpr/mgq002 Applying the Kelly criterion to lawsuits TRISTAN BARNETT Faculty of Business and Law, Victoria
More informationStatistical estimation using confidence intervals
0894PP_ch06 15/3/02 11:02 am Page 135 6 Statistical estimation using confidence intervals In Chapter 2, the concept of the central nature and variability of data and the methods by which these two phenomena
More informationUSTA TENNIS RULES CHALLENGE FOR TEACHING PROFESSIONALS AND COACHES *****************************************
USTA TENNIS RULES CHALLENGE FOR TEACHING PROFESSIONALS AND COACHES ***************************************** INSTRUCTIONS THIS TEST IS BASED UPON THE 2013 EDITION OF THE ITF RULES OF TENNIS AND THE CODE
More informationBellevue Club Cup Tennis Guidelines 2016-2017
Bellevue Club Cup Tennis Guidelines 2016-2017 Ladies Cup Team Tennis is a competitive interclub league with teams at six different levels: Evergreen, Emerald, Classic, Rainier, Challenge and Kingco. All
More information3.2 Roulette and Markov Chains
238 CHAPTER 3. DISCRETE DYNAMICAL SYSTEMS WITH MANY VARIABLES 3.2 Roulette and Markov Chains In this section we will be discussing an application of systems of recursion equations called Markov Chains.
More informationSCORESHEET INSTRUCTIONS. RALLY POINT SCORING (RPS 2 out of 3 sets)
RALLY POINT SCORING (RPS 2 out of 3 sets) 1. BEFORE THE MATCH a) On the upper part of the first page of the scoresheet 1.1 Name of the competition 1.2 Match number (from the daily schedule): 1.3 Site (city)
More informationFormula One Race Strategy
Formula One Race Strategy McLaren Racing Limited Sports Technology McLaren is a registered trademark of McLaren Racing Limited INTRODUCTION Figure 1: A Vodafone McLaren Mercedes driven by Lewis Hamilton
More informationMicroeconomics Sept. 16, 2010 NOTES ON CALCULUS AND UTILITY FUNCTIONS
DUSP 11.203 Frank Levy Microeconomics Sept. 16, 2010 NOTES ON CALCULUS AND UTILITY FUNCTIONS These notes have three purposes: 1) To explain why some simple calculus formulae are useful in understanding
More informationIII. TEAM COMPOSITION
Volleyball Rules I. GAME CHARACTERISTICS 1. Volleyball is a sport played by two teams on a playing court divided by a net. There are different, versions available for specific circumstances in order to
More information2016 NJSIAA/New Balance WOMENS TENNIS SINGLES/DOUBLES CHAMPIONSHIPS
NEW JERSEY STATE INTERSCHOLASTIC ATHLETIC ASSOCIATION 1161 Route 130, P.O. Box 487 Robbinsville, N.J. 08691 2016 NJSIAA/New Balance WOMENS TENNIS SINGLES/DOUBLES CHAMPIONSHIPS SINGLES Tennis ENTRY GUIDELINES
More informationBEACH VOLLEYBALL SHORT COURT RULES
Revised March 11, 2016 BEACH VOLLEYBALL SHORT COURT RULES City of Santa Barbara Parks & Recreation beach volleyball leagues are designed to be competitive and FUN. Referees are not provided and therefore
More information73rd Annual Tennis Championships. Up to maximum $500 for Open Singles Winner!
NSW Chinese Tennis Association Inc. Established since 1936 affiliated with Tennis NSW ABN 91023650964 73rd Annual Tennis Championships Website: www.nswcta.org.au (Information & Entry form) 紐 省 華 人 網 球
More informationLesson 1. Key Financial Concepts INTRODUCTION
Key Financial Concepts INTRODUCTION Welcome to Financial Management! One of the most important components of every business operation is financial decision making. Business decisions at all levels have
More informationMath 202-0 Quizzes Winter 2009
Quiz : Basic Probability Ten Scrabble tiles are placed in a bag Four of the tiles have the letter printed on them, and there are two tiles each with the letters B, C and D on them (a) Suppose one tile
More informationInferring Tennis Match Progress from In-Play Betting Odds
Department of Computing, Imperial College London Inferring Tennis Match Progress from In-Play Betting Odds Author: Xinzhuo Huang Supervisor: Dr. William Knottenbelt Second Marker: Dr. Jeremy Bradley June
More informationUSTA Middle States Sectional Tournaments Points Tables
USTA Middle States Sectional Tournaments Points Tables The points table is for Section L3, L4 & L5, as well as National L1, L2 & L3 The Sectional Points table below is based on the level of tournament
More informationMath 728 Lesson Plan
Math 728 Lesson Plan Tatsiana Maskalevich January 27, 2011 Topic: Probability involving sampling without replacement and dependent trials. Grade Level: 8-12 Objective: Compute the probability of winning
More informationPREDICTING THE MATCH OUTCOME IN ONE DAY INTERNATIONAL CRICKET MATCHES, WHILE THE GAME IS IN PROGRESS
PREDICTING THE MATCH OUTCOME IN ONE DAY INTERNATIONAL CRICKET MATCHES, WHILE THE GAME IS IN PROGRESS Bailey M. 1 and Clarke S. 2 1 Department of Epidemiology & Preventive Medicine, Monash University, Australia
More informationUsing the Solver add-in in MS Excel 2007
First version: April 21, 2008 Last revision: February 22, 2011 ANDREI JIRNYI, KELLOGG OFFICE OF RESEARCH Using the Solver add-in in MS Excel 2007 The Excel Solver add-in is a tool that allows you to perform
More informationSample Questions with Explanations for LSAT India
Five Sample Analytical Reasoning Questions and Explanations Directions: Each group of questions in this section is based on a set of conditions. In answering some of the questions, it may be useful to
More informationA Little Set Theory (Never Hurt Anybody)
A Little Set Theory (Never Hurt Anybody) Matthew Saltzman Department of Mathematical Sciences Clemson University Draft: August 21, 2013 1 Introduction The fundamental ideas of set theory and the algebra
More informationAn Automated Test for Telepathy in Connection with Emails
Journal of Scientifi c Exploration, Vol. 23, No. 1, pp. 29 36, 2009 0892-3310/09 RESEARCH An Automated Test for Telepathy in Connection with Emails RUPERT SHELDRAKE AND LEONIDAS AVRAAMIDES Perrott-Warrick
More informationUSA Volleyball Scorer Test A
Exam Instructions and Information: Read each question thoroughly and answer each question on the attached answer sheet using current 2011-13 USA Volleyball Domestic Competition Regulations and the Scoring
More informationParental Occupation Coding
Parental Occupation Coding A report submitted to the Performance Measurement and Reporting Taskforce of the Ministerial Council on Education, Employment Training and Youth Affairs by Dr Roger Jones Quantitative
More informationMachine Learning for the Prediction of Professional Tennis Matches
Imperial College London MEng Computing Final year project Machine Learning for the Prediction of Professional Tennis Matches Author: Supervisor: Dr. William Knottenbelt June 15, 2015 Abstract Extensive
More informationConstruction Administrators Work Smart with Excel Programming and Functions. OTEC 2014 Session 78 Robert Henry
Construction Administrators Work Smart with Excel Programming and Functions OTEC 2014 Session 78 Robert Henry Cell References C O P Y Clicking into the Formula Bar or the Active Cell will cause color coded
More informationThe GMAT Guru. Prime Factorization: Theory and Practice
. Prime Factorization: Theory and Practice The following is an ecerpt from The GMAT Guru Guide, available eclusively to clients of The GMAT Guru. If you would like more information about GMAT Guru services,
More informationQ&As: Microsoft Excel 2013: Chapter 2
Q&As: Microsoft Excel 2013: Chapter 2 In Step 5, why did the date that was entered change from 4/5/10 to 4/5/2010? When Excel recognizes that you entered a date in mm/dd/yy format, it automatically formats
More informationFundamentals of Probability
Fundamentals of Probability Introduction Probability is the likelihood that an event will occur under a set of given conditions. The probability of an event occurring has a value between 0 and 1. An impossible
More information1) Course Entry Requirement(s) To gain entry to the Diploma of Higher Education in Information Technology prospective students must have:
JCU Diploma of Higher Education (Information Technology) COURSE DETAILS 1) Course Entry Requirement(s) To gain entry to the Diploma of Higher Education in Information Technology prospective students must
More informationReferee Analytics: An Analysis of Penalty Rates by National Hockey League Officials
Referee Analytics: An Analysis of Penalty Rates by National Hockey League Officials Michael Schuckers ab, Lauren Brozowski a a St. Lawrence University and b Statistical Sports Consulting, LLC Canton, NY,
More informationWho wins the rest of the match European handicap Home t.win or Away t. win after regular time/overtime/penalty shootout Which team will win
Bet Smart Live Odds via XML is an automated odds service for direct and customer use. Bet Smart inteligent betting system can automatically set, update and change and close your bets or send data via XML
More informationFairfield Public Schools
Mathematics Fairfield Public Schools AP Statistics AP Statistics BOE Approved 04/08/2014 1 AP STATISTICS Critical Areas of Focus AP Statistics is a rigorous course that offers advanced students an opportunity
More informationTeachers should read through the following activity ideas and make their own risk assessment for them before proceeding with them in the classroom.
Mathematical games Teacher notes Teachers should read through the following activity ideas and make their own risk assessment for them before proceeding with them in the classroom. Aims: To use mathematics
More informationParalympic Table Tennis
ENGLISH FOR THE GAMES Paralympic Table Tennis When athletes come together from around the world to compete in the Olympic and Paralympic Games, they are fulfilling their dreams and competing at the highest
More informationEffects of expertise on football betting
Effects of expertise on football betting Yasser.khazaal@hcuge.ch Geneva Hospital University, Department of Addictology INTRODUCTION Maher 2006 Football is one of the most popular sports in the world. It
More informationMULTIPLE REGRESSION WITH CATEGORICAL DATA
DEPARTMENT OF POLITICAL SCIENCE AND INTERNATIONAL RELATIONS Posc/Uapp 86 MULTIPLE REGRESSION WITH CATEGORICAL DATA I. AGENDA: A. Multiple regression with categorical variables. Coding schemes. Interpreting
More informationSECTION 8: PROMOTIONS FOR LIVE ODDS IN SPORTS COVERAGE...
CODE OF PRACTICE TABLE OF CONTENTS SECTION 8: PROMOTIONS FOR LIVE ODDS IN SPORTS COVERAGE... 2 Objective... 2 Scope... 2 Promotion of Live Odds during a Live Sporting Event... 4 Promotion of Live Odds
More informationScientific Graphing in Excel 2010
Scientific Graphing in Excel 2010 When you start Excel, you will see the screen below. Various parts of the display are labelled in red, with arrows, to define the terms used in the remainder of this overview.
More informationTest Positive True Positive False Positive. Test Negative False Negative True Negative. Figure 5-1: 2 x 2 Contingency Table
ANALYSIS OF DISCRT VARIABLS / 5 CHAPTR FIV ANALYSIS OF DISCRT VARIABLS Discrete variables are those which can only assume certain fixed values. xamples include outcome variables with results such as live
More informationPractice Problems for Homework #8. Markov Chains. Read Sections 7.1-7.3. Solve the practice problems below.
Practice Problems for Homework #8. Markov Chains. Read Sections 7.1-7.3 Solve the practice problems below. Open Homework Assignment #8 and solve the problems. 1. (10 marks) A computer system can operate
More informationFINANCIAL ANALYSIS GUIDE
MAN 4720 POLICY ANALYSIS AND FORMULATION FINANCIAL ANALYSIS GUIDE Revised -August 22, 2010 FINANCIAL ANALYSIS USING STRATEGIC PROFIT MODEL RATIOS Introduction Your policy course integrates information
More informationMeasuring Evaluation Results with Microsoft Excel
LAURA COLOSI Measuring Evaluation Results with Microsoft Excel The purpose of this tutorial is to provide instruction on performing basic functions using Microsoft Excel. Although Excel has the ability
More informationENGLISH SCHOOLS' TABLE TENNIS ASSOCIATION - INDIVIDUAL KNOCKOUT - 16 PLAYERS
ENGLISH SCHOOLS' TLE TENNIS SSOCITION - INDIVIDUL KNOCKOUT - 16 PLYERS First Round Quarter Finals Semi Finals Match 1 Match 2 Match 3 Match 4 Final Match 5 Match 6 Match 7 Match 8 ENGLISH SCHOOLS' TLE
More informationLevel. Two-handed striking
HEALTH AND PHYSICAL EDUCATION YEARS 1 TO 10 SOURCEBOOK MODULE HEALTH AND PHYSICAL EDUCATION MIDDLE PRIMARY Level F 1 2 3 4 5 6 B6 3 Two-handed striking Strands Developing Concepts and Skills for Physical
More informationJan Vecer Tomoyuki Ichiba Mladen Laudanovic. Harvard University, September 29, 2007
Sports Sports Tomoyuki Ichiba Mladen Laudanovic Department of Statistics, Columbia University, http://www.stat.columbia.edu/ vecer Harvard University, September 29, 2007 Abstract Sports In this talk we
More informationPart 1 will be selected response. Each selected response item will have 3 or 4 choices.
Items on this review are grouped by Unit and Topic. A calculator is permitted on the Algebra 1 A Semester Exam The Algebra 1 A Semester Exam will consist of two parts. Part 1 will be selected response.
More informationMANAGEMENT OPTIONS AND VALUE PER SHARE
1 MANAGEMENT OPTIONS AND VALUE PER SHARE Once you have valued the equity in a firm, it may appear to be a relatively simple exercise to estimate the value per share. All it seems you need to do is divide
More informationClass 19: Two Way Tables, Conditional Distributions, Chi-Square (Text: Sections 2.5; 9.1)
Spring 204 Class 9: Two Way Tables, Conditional Distributions, Chi-Square (Text: Sections 2.5; 9.) Big Picture: More than Two Samples In Chapter 7: We looked at quantitative variables and compared the
More informationSCORESHEET INSTRUCTIONS. RALLY POINT SCORING (RPS 2 out of 3 sets)
RALLY POINT SCORING (RPS 2 out of 3 sets) 1. BEFORE THE MATCH a) On the upper part of the first page of the scoresheet 1.1 Name of the competition 1.2 Match number (from the daily schedule): 1.3 Site (city)
More informationMAT 183 - Elements of Modern Mathematics Syllabus for Spring 2011 Section 100, TTh 9:30-10:50 AM; Section 200, TTh 8:00-9:20 AM
MAT 183 - Elements of Modern Mathematics Syllabus for Spring 2011 Section 100, TTh 9:30-10:50 AM; Section 200, TTh 8:00-9:20 AM Course Instructor email office ext. Thomas John, Ph.D. thjohn@syr.edu 224
More informationGraphing Parabolas With Microsoft Excel
Graphing Parabolas With Microsoft Excel Mr. Clausen Algebra 2 California State Standard for Algebra 2 #10.0: Students graph quadratic functions and determine the maxima, minima, and zeros of the function.
More informationVOLLEYBALL. Information SOMI-Specific Sport season: April-June
VOLLEYBALL Culminating State Event State Summer Games Events Offered Skills Team Competition Modified Team Competition Unified Team Competition National Governing Body Federation Internationale de Volleyball
More informationMu2108 Set Theory: A Gentle Introduction Dr. Clark Ross
Mu2108 Set Theory: A Gentle Introduction Dr. Clark Ross Consider (and play) the opening to Schoenberg s Three Piano Pieces, Op. 11, no. 1 (1909): If we wish to understand how it is organized, we could
More informationJournal of Student Success and Retention Vol. 2, No. 1, October 2015 THE EFFECTS OF CONDITIONAL RELEASE OF COURSE MATERIALS ON STUDENT PERFORMANCE
THE EFFECTS OF CONDITIONAL RELEASE OF COURSE MATERIALS ON STUDENT PERFORMANCE Lawanna Fisher Middle Tennessee State University lawanna.fisher@mtsu.edu Thomas M. Brinthaupt Middle Tennessee State University
More informationState of the Art Virtual Portfolio Management: Building Skills that Matter
State of the Art Virtual Portfolio Management: Building Skills that Matter There are many ways for students to play stock market games or more generally, participate in a virtual portfolio simulation:
More informationwww.auditexcel.co.za
Spreadsheet Professional Quick Start Guide Contact Details Adrian Miric Mobile: +27 83 272 2552-1 - Introduction The aim of this document is too give you a quick introduction on using Spreadsheet Professional.
More informationOBSERVATIONS FROM 2010 INSPECTIONS OF DOMESTIC ANNUALLY INSPECTED FIRMS REGARDING DEFICIENCIES IN AUDITS OF INTERNAL CONTROL OVER FINANCIAL REPORTING
1666 K Street, N.W. Washington, DC 20006 Telephone: (202) 207-9100 Facsimile: (202) 862-8430 www.pcaobus.org OBSERVATIONS FROM 2010 INSPECTIONS OF DOMESTIC ANNUALLY INSPECTED FIRMS REGARDING DEFICIENCIES
More informationLesson Plans for (9 th Grade Main Lesson) Possibility & Probability (including Permutations and Combinations)
Lesson Plans for (9 th Grade Main Lesson) Possibility & Probability (including Permutations and Combinations) Note: At my school, there is only room for one math main lesson block in ninth grade. Therefore,
More informationSCRATCH Lesson Plan What is SCRATCH? Why SCRATCH?
SCRATCH Lesson Plan What is SCRATCH? SCRATCH is a programming language that makes it easy to create interactive stories, animations, games, music, and art that can then easily be shared on the web. Scratch
More informationRating Systems for Fixed Odds Football Match Prediction
Football-Data 2003 1 Rating Systems for Fixed Odds Football Match Prediction What is a Rating System? A rating system provides a quantitative measure of the superiority of one football team over their
More informationAn Activity-Based Costing Assessment Task: Using an Excel Spreadsheet
e-journal of Business Education & Scholarship of Teaching Vol. 3, No. 1, 2009, pp:25-35. http://www.ejbest.org Instructional Note An Activity-Based Costing Assessment Task: Using an Excel Spreadsheet Damian
More informationComputational Geometry Lab: FEM BASIS FUNCTIONS FOR A TETRAHEDRON
Computational Geometry Lab: FEM BASIS FUNCTIONS FOR A TETRAHEDRON John Burkardt Information Technology Department Virginia Tech http://people.sc.fsu.edu/ jburkardt/presentations/cg lab fem basis tetrahedron.pdf
More informationMATH ADVISEMENT GUIDE
MATH ADVISEMENT GUIDE Recommendations for math courses are based on your placement results, degree program and career interests. Placement score: MAT 001 or MAT 00 You must complete required mathematics
More informationSelf-directed learning: managing yourself and your working relationships
ASSERTIVENESS AND CONFLICT In this chapter we shall look at two topics in which the ability to be aware of and to manage what is going on within yourself is deeply connected to your ability to interact
More informationCHAPTER 18 Programming Your App to Make Decisions: Conditional Blocks
CHAPTER 18 Programming Your App to Make Decisions: Conditional Blocks Figure 18-1. Computers, even small ones like the phone in your pocket, are good at performing millions of operations in a single second.
More informationHow to Calculate the Probabilities of Winning the Eight LUCKY MONEY Prize Levels:
How to Calculate the Probabilities of Winning the Eight LUCKY MONEY Prize Levels: LUCKY MONEY numbers are drawn from two sets of numbers. Four numbers are drawn from one set of 47 numbered white balls
More informationAN ANALYSIS OF A WAR-LIKE CARD GAME. Introduction
AN ANALYSIS OF A WAR-LIKE CARD GAME BORIS ALEXEEV AND JACOB TSIMERMAN Abstract. In his book Mathematical Mind-Benders, Peter Winkler poses the following open problem, originally due to the first author:
More informationGOLF COMPETITIONS AND HOW THEY ARE PLAYED Golf Australia Advice (Version 20 February 2013)
GOLF COMPETITIONS AND HOW THEY ARE PLAYED Golf Australia Advice (Version 20 February 2013) These notes are only intended to assist in the general concept of how various competitions are played. They must
More information